Preheat oven to 375 degrees (180°C). Grease a 15×10 inch jelly-roll pan; line with parchment paper. Grease and flour paper; set aside. Spread out a clean, thin dish towel on the counter (make sure the towel is larger than your jelly roll pan); sprinkle liberally with powdered sugar (this can be done using a mesh strainer).

In a small bowl, whisk together flour, baking powder, baking soda. In a large bowl combine eggs and sugar; beat until thickened. Add bananas and vanilla; beat until well mixed. Stir in flour mixture into egg mixture. Spread batter evenly into prepared pan, easing it carefully to the corners with a spatula.

Bake for 13-15 minutes or until center springs back when lightly touched.